Results 1 to 3 of 3

Math Help - magic circles?

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    4

    magic circles?

    Can anyone help me understand how to arrange the digits (odd only) 9-25 in a magic circle so that the sum of the numbers in each straight line is the same? There is one circle inthe middle and 8 around it. There must be a formula to this. Thank you.
    Last edited by gager23; November 17th 2008 at 12:49 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    645
    Hello, gager23!


    Arrange the odd numbers from 9 to 25 in a magic circle
    so that the sum of the numbers in each straight line is the same.
    There is one circle inthe middle and 8 around it.
    There really isn't any formula for this, but there is a very logical procedure.


    \text{We have the numbers: }\;9, 11,13,15,\underbrace{17}_{\uparrow},19,21,23,25
    Isn't it reasonable to put the middle number in the center of the circle?


    Next, take pairs of numbers "from each end": . (9,25),\:(11,23),\:(13,21),\:(15,19)
    . .
    Note that the pairs have the same sum: 34.

    Place the pairs on opposite ends of a diameter.


    Then one possible solution looks like this:
    Code:
                  * 9 *
              *     |     *
           19       |       11
           *  \     |     /  *
                \   |   /
          *       \ | /       *
         21 - - - -17 - - - - 13
          *       / | \       *
                /   |   \
           *  /     |     \  *
           23       |       15
              *     |     *
                  *25 *
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    4

    magic circle

    Thanks for the reply--it makes sense and is appreciated.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Magic Squares with Magic "Subsquares"
    Posted in the Number Theory Forum
    Replies: 14
    Last Post: July 9th 2010, 10:21 AM
  2. Prove that every rigid motion transforms circles into circles
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: February 11th 2010, 06:00 PM
  3. Replies: 2
    Last Post: October 6th 2009, 08:04 AM
  4. Magic Hexagons
    Posted in the Math Challenge Problems Forum
    Replies: 1
    Last Post: June 10th 2008, 03:44 AM
  5. magic square
    Posted in the Number Theory Forum
    Replies: 18
    Last Post: September 29th 2006, 10:00 PM

Search Tags


/mathhelpforum @mathhelpforum